# beta(), betaf() and betal() functions in C++ STL

The beta(), betaf() and betal() are built-in functions in C++ STL that are used to compute the beta functionof two positive real values. The function takes two variables x and y as input and returns the beta function of x and y. Beta function (Also known as Euler integral of first kind) of x and y can be defined as:

Syntax

double beta(double x, double y)
or
long double betal(long double x, long double y)
or
float betaf(float x, float y)

Parameters: The function accepts two mandatory parameters x and y which specifies the values of a floating-point or integral type. The parameters can be of double, double or float, float or long double, long double data-type.

Return Value: The function returns the value of beta function of x and y. The return type depends on the parameters passed. It is same as that of the parameter.

Note: The function runs in and above C++ 17(7.1).

Below program illustrates the beta(), betaf() and betal() functions:

 // C++ program to illustrate the three functions  // Being a special function, beta is only guaranteed  // to be in cmath if the user defines  //  __STDCPP_WANT_MATH_SPEC_FUNCS__ before including  // any standard library headers.  #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1  #include  using namespace std;     int main()  {      // Computes the beta function of 5 and 4 and print it      // If provided arguments are not of type double      // they are implicitly type-casted to the higher type.         // first example of beta()      cout << beta(5, 4) << "\n";         // second example of betaf()      cout << betaf(10.0, 4.0) << "\n";         // third example of betal()      cout << betal(10.0, 6.7) << "\n";      return 0;  }

Output:

0.00357143
0.00034965
1.65804e-005


Application of Beta function: It is used to compute Binomial Coefficients.The binomial coefficient in terms of beta function can be expressed as:

The above relation can be used to compute the binomial coeeficient. An illustration has been shown below:

 // C++ program to print the pascal triangle  // Being a special function, beta is only guaranteed  // to be in cmath if the user defines  //  __STDCPP_WANT_MATH_SPEC_FUNCS__ before including  // any standard library headers.  #define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1  #include  #include  using namespace std;     // Function to return the value of binomial Coefficient  double binomialCoefficient(int n, int k)  {      // Calculate the value of nCr using above formula.      double ans = 1 / ((n + 1) * beta(n - k + 1, k + 1));      return ans;  }  // Driver Code  int main()  {      // Print the binomial Coefficient nCr where n=5 and r=2      cout << binomialCoefficient(5, 2) << "\n";         return 0;  }

Output:

10


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